How can I move separate edges towards each other at the same time?
They seem to be aligned along the world x axis, so with the selection shown, hit S, Y and move the mouse. Pressing 0  will make them form one line through their exact center, which should be the x-axis.
If they are not aligned to a world axis, switch the transform orientation to normal first, edges have normals, too, they are not as reliable as the ones of faces, but more often than not, they get the job done.